Hybrid inertial/magnetic system for determining the position and orientation of a mobile body

ABSTRACT

The present invention concerns a system for contactless determination of the position and orientation of a first mobile object (M) relative to a reference mark (RP) carried by a second fixed or mobile object (P), in a disturbed electromagnetic environment comprising a transmitting antenna (E) with ferromagnetic cores (E-1) having magnetic permeability higher than 10, incorporating sensors (E-3) for measuring the magnetic field Xu actually emitted by the axes of the ferromagnetic cores. A means (4-4) for extracting the signal correlated with the ambient noise XBR (Tk−KbTe)—from the sensors (Sb) fixed in the platform (P), forms, with measurement Xu of the emitted magnetic induction, a complete model of the measured fields, making it possible to extract, without errors, the six parameters relative to the field model without disturbances.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a national phase entry under 35 U.S.C. § 371 ofInternational Patent Application PCT/FR2014/052843, filed Nov. 6, 2014,designating the United States of America and published as InternationalPatent Publication WO 2015/067903 A1 on May 14, 2015, which claims thebenefit under Article 8 of the Patent Cooperation Treaty to FrenchPatent Application Serial No. 1302566, filed Nov. 6, 2013.

TECHNICAL FIELD

The field of the invention is the measurement of the position andorientation of a mobile body M, which moves in translation and rotationrelative to a reference mark connected to a fixed or mobile structure Prelative to an inertial reference frame fixed-type reference mark. Inparticular, the invention concerns the determination of the position andorientation (P/O) of the helmet of a pilot in the reference mark of anaircraft, P/O from which the angular position of an external target isdetermined in the same mark by sight through a system including thehelmet-mounted display of the pilot. In a known manner, the pilotsuperimposes on the external target the image of a collimated crossprojected on the transparent visor thereof, and acquires the measurementtaken by the device by pressing on a push-button.

More specifically, concerning the devices for determining the P/O,called “trackers of magnetic technology,” the main problem ofdetermining the position and orientation of a mobile body relative to areference mark connected to a fixed or mobile structure having to beaccurately determined comes from an electromagnetic environmentsignificantly disturbed by radiated magnetic fields (“EMI” forElectromagnetic Interferences, “ECI” for Eddy Current Interferences orfields due to Eddy currents) and/or magnetic fields induced byferromagnetic bodies (“FMI” for FerroMagnetic Interferences),environments such as the cockpits of aircraft and, more specifically, ofhelicopters, surgical operating rooms, etc. Thus, the accuracy issignificantly degraded in the presence of the interferences. Therefore,the problem consists of finding the means to improve the performancesdespite the disturbances.

BACKGROUND

U.S. Pat. No. 7,640,106 is known in prior art describing an apparatusfor determining the position of a selected object relative to a movingreference image, the apparatus including at least one reference frametransceiver assembly secured to the moving reference frame, at least oneobject transceiver assembly firmly attached to the selected object, aninertial measurement unit firmly attached to the selected object, aninertial navigation system (“INS”) secured to the moving referenceimage, and a tracking processor coupled with the object transceiverassembly, to the inertial measurement unit and to the inertialnavigation system, the object transceiver assembly communicating withthe reference frame transceiver assembly using magnetic fields, theinertial measurement unit producing IMU inertial measurements of motionof the selected object relative to an inertially fixed reference frame,the inertial navigation system producing INS inertial measurements ofmotion of the moving reference frame relative to the inertially fixedreference frame, the tracking processor receiving electromagneticmeasurements resulting from the magnetic communication between thereference frame transceiver assembly and the object transceiverassembly, the tracking processor determining the position of theselected object relative to the moving reference frame by using the IMUinertial measurements and the INS inertial measurements to optimize theelectromagnetic measurements.

French Patent FR2807831 is also known in prior art describing a devicefor measuring the position and orientation of a mobile object relativeto a fixed structure, in a disturbed magnetic environment, including:

-   -   a first assembly of orthogonal coils emitting magnetic fields,        secured to the fixed structure, defining a reference mark;    -   a second assembly of orthogonal coils receiving magnetic        field(s), secured to the object, and forming a sensor, each of        the coils belonging to a sensor channel.

Such a device includes means:

-   -   for simultaneous and continuous field emission, on the coils of        the first assembly;    -   for measuring, on the sensor channels, the vector sum of the        emitted fields and of the disturbance fields generated by the        environment;    -   for evaluating the disturbance fields;    -   for estimating fields emitted in an undisturbed environment by        suppressing the evaluated disturbance fields from the vector        sum; and    -   for computing the position and orientation of the object in the        reference mark.

U.S. Pat. No. 5,646,525 describes another example of equipment fordetermining the position and orientation of a helmet worn by a crewmember in a vehicle including a generator, associated with the vehicle,which produces a rotating magnetic and electric field of fixed strength,the orientation and frequency within at least a portion of the vehicle.The apparatus also includes a plurality of detectors, each of whichgenerates a signal proportional to at least one of the electric ormagnetic fields, at least one point associated with the helmet andcalculation circuitry responsive to the signal for determining thecoordinates of the at least one point relative to the generator and fordetermining the position and orientation of the helmet.

U.S. Pat. No. 6,400,139 also describes an example of an apparatus forposition/orientation tracking within a bounded volume. The methods andapparatus employ at least one fixed sensor, called a “witness sensor,”having a fixed position and orientation near or within the volume toaccount for electromagnetic distortion. One or more probe sensors areplaced on an object having to be tracked within the volume, and theoutput of each witness sensor is used to compute the parameters of anon-real effective electromagnetic source. The parameters of theeffective source are used as inputs for the computation of the positionand orientation measured by each probe sensor, as if the object were inthe non-distorted electromagnetic field produced by the effective sourceor sources. In addition to trackers for the helmet-mounted displays inaircraft, tank, and armored-vehicle applications, the invention findsutility in any electromagnetic tracking system that might be subject toelectromagnetic distortion or interference.

In general, the solutions of prior art do not teach solutions tocompensate for the disturbances not correlated with the transmitters(actual emitted fields).

U.S. Pat. No. 7,640,106 requires a first inertial sensor in the helmetand a second inertial sensor and an estimator (Kalman filter) fordetermining an orientation of an object. The solution requires providinga sensor on the fixed platform in order to determine the angularorientation of the helmet in the mark of the platform by incorporatingthe estimated relative velocity. Relative velocity is obtained bymeasuring the difference between:

-   -   the angular velocity of the mobile body measured at the output        of an IMU angular velocity sensor attached to the mobile body,        the orientation of which is to be determined, measured in a        fixed inertial frame (inertial reference frame); and    -   the angular velocity of the inertial platform measured by an        INS-type inertial unit.

The solution, therefore, requires a double inertial system, doubling thenoise and the errors.

Furthermore, the solution does not take into account the strongelectromagnetic disturbances observed in a real cell, for example, ahelicopter or airplane cell.

Furthermore, the solution requires an estimation to be carried out ofthe angular velocity.

The solution taught by U.S. Pat. No. 6,400,139 includes theinterpolation of data coming from a plurality of sensors in view ofcreating a model of the fields sent by real sources, and modellingunknown or dummy sources to compensate the Eddy current disturbances.The solution consists of installing a plurality of fixed witness sensorsin the vicinity of the volume in which the mobile body moves, in orderto construct a model of the field measured by the witness sensors. Themodel is used for recomputing by interpolation the field measured by thesensor positioned on the mobile object, which does not make it possibleto compensate the disturbance fields of Eddy currents, nor does it makeit possible to process the disturbances of radiated and non-correlateddisturbances (EMI). Only the ECI-type disturbances are correlated withthe emitted radiative field.

All of the solutions of prior art require the use of an additionalinertial platform to determine an additional mark in addition to thereference system provided by the inertial system of the aircraft, whichcomplicates the implementation and the errors.

BRIEF SUMMARY

The object of the disclosure relates to a system aiming to remedy thedisadvantages of the prior art and to establish a method and produce aprocess for eliminating electromagnetic disturbances (ECI: Eddycurrents, FMI: induced ferromagnetism) in real time without requiringthe very expensive need to map the effective volume scanned by thesensor.

Another aim of the disclosure is to improve the signal-to-noise S/Nratio of the P/O detector for obtaining the required performances inenvironments significantly disturbed by EMI (for example, in aircraftand, more specifically, in helicopters: radiated fields created byon-board generators and on-board equipment). The signal-to-noise S/Nratio may be expressed as the ratio between the standard deviation ofthe signal Sc received by the sensor in “free space,” i.e., without anyelectromagnetic disturbance and the standard deviation of the noise B,the noise being the sum of all of the signals not coming directly fromthe transmitter (inductive field).

The purpose of the disclosure is to achieve an improvement of the S/Nratio in the order of 1000 for the most critical cases (helicopters).

A third aim of the disclosure is to compensate the latency of the outputinformation through hybridization with an inertial system.

By referring to FIGS. 2, 3 and 4, which will subsequently be explained,it is indicated that functions of the disclosure:

-   -   Deploy an optimized transmitter E in the following directions:        -   Generation of alternating currents by E-2 according to a            specific temporal pattern on a finished temporal support and            being repeated sequentially. The pattern is preferably a            Pseudo-Random Binary Sequence (PRBS) generated by E-4 of the            processor 4.        -   Multiplication by three to ten of the signal emitted            relative to the transmitters of prior art (comparable            reference distance, volume). The method consists of            optimizing the winding shapes of the transmission axes to            increase the number of turns for a given diameter of wire            and to introduce a core of very permeable material of            specific shape for increasing the induction emitted in            ratios higher than 10:E-1.        -   Reduction of the total power and, in particular, the power            lost by Joule effect, which increases the temperature and            may cause the results to shift (expansions, deformations,            etc.), which amounts to reducing the emission current.        -   Control E-2 of the system in magnetic field as a result of            sensors E-3 (also known as “sensors_E”) being included in            the coils of the transmission axes.        -   Control of the magnetization of the magnetic coils by            measurement of the symmetry of the alternating currents            injected by E-1-2.    -   Measure the total field by a sensor with Ne axes C-1, the        bandwidth of which ranges from a few tens to a few thousands of        Hertz, the output Sc of which is at Ne components.    -   Acquire by the processor 4 the data Xu from E, Sc from C-1, Sp        from C-2, {right arrow over (ω)} angular velocity of the object        M and A=ψ, θ, φ the attitudes of the platform both from C-3, all        of the inertial measurements.    -   Filter the various disturbances (noises) of Sc (measurement of        the sensor_C from C-1), i.e., the radiated disturbances (EMI),        the disturbances created by the Eddy currents (ECI for Eddy        Current Interferences) circulating in the conductors situated in        a close volume and caused by the variable fields emitted by the        transmitter, as well as the FerroMagnetic effects (FMI for        FerroMagnetic Interferences):        -   The noised signal Sc is measured by the receiving assembly            C-1, the noise Sp is measured and estimated from the            measuring device C-2. It will subsequently be described            that, in a particular embodiment, according to the            conditions of the environment, the noise may be estimated            from the device C-1, preferably over a time during which no            current is sent into the coils E-1 by E-4.        -   The filtering, subsequently explained in a first embodiment,            is performed in the processor 4-4 by constructing a temporal            model of the preceding disturbances and by estimating            therefrom the parameters using an optimal or sub-optimal            filter in real time over short times T_(off) during which            the currents injected into coils E-1 are zero. The variables            of the model are magnitudes varying over time, independent            or weakly correlated from the statistical point of view that            make it possible to show the variations of useful signals            and noises. In a second embodiment, an embodiment of the            ambient noise S_(b) is measured by a sensor block C2, a            complete model of which is modelled as previously. The            parameters of the model are used to eliminate by subtraction            all of the components of S_(b) correlated with the fields            emitted by coils E-1. Thus, the non-correlated noise is            extracted to become an independent variable of the linear            magnetic model of the signals measured by the sensor C-1            attached to M.        -   Determine, from all of the parameters identified, the            parameters of the single model of the fields emitted by the            axes of the transmitter (field known as undisturbed “free            space”) and, in particular, the matrix for computing in a            known manner the position and orientation of the mobile            object.    -   Improve the dynamic behavior of the detector, in particular, by        minimizing the latency of the detector, i.e., the time between        the real instant of occurrence of an event over the magnitude to        be measured and the detection thereof by the P/O determination        system. The improvement is made through hybridization of the        preceding magnetic detection with an inertial assembly for        measuring the angular velocities of the mobile object and use of        the attitudes of the inertial unit of the platform.

In the disclosure, which will subsequently be described in more detail,the currents injected into the windings that create the inductions, arepreferably simultaneous. The measured inductions are, therefore, the sumof the fields emitted at instant t and the fields present in theenvironment. Therefore, the aim of the disclosure is to distinguish inthe measured field each component emitted by each transmission axis. Therecognition of the field emitted by one of the components constitutesdemultiplexing of the inductions that can be functionally qualified bycomparison with the inventions cited that either perform temporaldemultiplexing (emission not simultaneous but sequenced over time) orfrequential demultiplexing (detection of frequencies in the spectralrange). When the fields are demultiplexed, it is considered that threeindependent emissions were received on three sensor axes.

With regard to the hybrid system, the principle of the disclosureconsists of using the attitude provided by the magnetic tracker meansexpressed in the fixed inertial frame to reset or initialize thecomputation of the attitude of the IMU gyrometric sensors obtained byincorporation into the inertial frame of a dynamic equation forpredicting a quaternion. The attitude of the tracker means expressed inthe inertial frame simply uses the attitude of the platform provided bythe INS, in the form of three Euler angles or DCM matrix (directioncosine matrix of the platform) or of the quaternion computed from theEuler angles or DCM matrix. The dynamic prediction model, computed athigh speed, is reset to time t-T_(L), T_(L) being the latency time ofthe magnetic tracker means, at each arrival of the quaternion providedby the magnetic tracker means. The information necessary for computingthe quaternion (in particular, the angular velocities of the IMU of themobile object) having been stored in memory over time T_(L), thequaternion prediction model is recomputed from time t-T_(L) up to thecurrent time t by using the velocities stored in memory. Beyond time tup to the next arrival of the magnetic tracker information, thequaternion is computed at the frequency for acquiring angular velocitymeasurements. The disclosure also comprises the real-time correction ofthe triaxial angular velocity sensor by estimation of the errors of thesensor.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure will be better understood upon reading thefollowing description, concerning non-limiting examples of embodimentsof the disclosure referring to the accompanying drawings where:

FIGS. 1A-1C show schematic views of solutions of prior art;

FIG. 2 shows a schematic view of the mark and object reference system;

FIGS. 3A and 3B show schematic views of the architecture of thedisclosure;

FIG. 4 shows a schematic view of the detailed architecture of thedisclosure;

FIG. 5 shows a schematic view of the control of the emitted inductions;

FIG. 6 shows a schematic view of a transmitter block of prior art;

FIG. 7 shows the schematic view of the formation of an axis E1 of thetransmitter according to the disclosure;

FIGS. 8A and 8B show examples of embodiments of transmission axes;

FIG. 9 shows a schematic view of a core installer according to thedisclosure;

FIGS. 10A and 10B show schematic views of the field control;

FIG. 11 shows the temporal transmission diagram; and

FIGS. 12A and 12B show schematic views of magnetic-inertialhybridization and an inertial extrapolator.

DETAILED DESCRIPTION

According to FIG. 2, the system for contactless determination of theposition and orientation (P/O) of a first object M, the associatedorthogonal mark R_(M) of which is mobile relative to a reference markcarried by a second object P (Platform), fixed or mobile relative to aninertial reference frame R_(i) of fixed orientation relative to thestars situated at the center of the earth. The device is arranged in adisturbed electromagnetic environment. A transmitter E consisting ofN_(i) coils forming a quasi-orthogonal mark R_(E) is rigidly attached tothe platform P. The transfer matrix R_(E/P) between transmitter markR_(E) and platform mark R_(P) is presumed constant and measured duringinstallation of the mechanical reference of the transmitter in theplatform P. When the mark R_(P) is mobile relative to R_(i), as is thecase when the platform is an aircraft, the mark R_(P) is defined in themark R_(i) by the Euler angles defining the attitude and computed by theinertial unit or an equivalent device and transmitted to the process ofthe disclosure. It should be noted that the quaternion Q_(PI) like thetransfer matrix R_(P/I) between R_(P) and R_(i) represent the attitudeof P relative to R_(i). On the mobile object M are rigidly attached themagnetic sensor with Nc quasi-orthogonal axes C-1 known as sensor_C andthe inertial sensor C-3-1 of three orthogonal axes angular velocities.The latter sensor is, for example, of MEMS (Micro-Electro-MechanicalSystems) type, which measures the angular velocities in its ownreference mark R_(gi), the orientation of which is presumed known by anin-factory measurement according to procedures known by the personskilled in the art. The sensor C-1 is a sensor for measuring themagnetic induction field of fluxgate, fluxmeter, controlled fluxmeter,Hall effect sensor, AMR, GMR, TMR, etc. The axes thereof are defined bythe transfer matrix R_(C/M) fixed and identified in the factory in aknown manner.

In the case of some applications for which the environments aresignificantly magnetically disturbed by EMI, a particular embodimentconsists of adding a certain number of sensors known as sensor_Brepresented by block C-2 in FIG. 3A. The sensors are attached to theplatform. The sensors are 1- to 3-axis sensors of the same type as themagnetic sensor C-1, and the number thereof is higher than or equalto 1. The orientation and position thereof may not be known accurately,which constitutes an advantage. These are placed at a sufficiently largedistance from the transmitter in the environment of the platform inorder to measure as little as possible the field emitted by thetransmitter E. The aim is to measure the EMI present in the environmentof the sensor C-1. Ideally, a single axis is sufficient but one or more1- to 3-axis sensors may have to be placed close to specific equipmentof the platform to measure harmful disturbances related to the item(s)of equipment.

General Architecture

FIG. 3B shows a schematic view of the hardware architecture of thesystem according to the disclosure.

The mobile body (M) is a helicopter pilot helmet, the cell of thehelicopter forming the platform (P).

On the helmet (M) are attached an electromagnetic sensor (C-1) and anIMU inertial sensor (C-3-1), the two sensors being mechanicallyconnected in a rigid manner to the helmet (M).

On the platform P are attached:

-   -   a transmitter E;    -   an inertial platform C-3-2; and    -   a reference electromagnetic sensor C2.

A computer (4-4) receives the signals from the various components andcarries out the processes described below.

FIG. 4 explains the assemblies known as “blocks” and shown in FIGS. 2and 3A:

A first assembly E for transmitting magnetic induction(s), comprising afirst transmitting sub-assembly E-1 of Ne, Ne being equal to at leasttwo transmitting coils, the axes of symmetry of which, not parallel withone another, form a mark R_(E) attached to the second object P.

A first receiving assembly C-1, attached to the mobile object M andcomprising Nc>=2 non-parallel receiving coils, forming a mark R_(C1),sensitive to the ambient magnetic field resulting from the vector sum ofthe fields emitted by the first transmitting assembly E and disturbingmagnetic fields generated by electric currents existing in theenvironment and by ferromagnetic magnetizations, the second assemblyforming a sensor C-1 secured to the first mobile object M and such thatthe product Nc*Ne>=6, the first mobile object M has a reference markR_(M). The orientation of the mark R_(C1) relative to the mark R_(M) isconstant and noted by R_(C1)/M the direction cosine matrix of the axesof C-1 in RM. The Nc components of SC form the output of the firstreceiving assembly C-1.

A computing processor 4 for computing the position and orientation ofthe first mobile object, coupled with the first analog/digitalconversion (or ADC) means 4-1 for carrying out the acquisition, atdiscrete times t_(k)=k*Te, of analog signals S_(c), X_(u1) and S_(b)according to FIG. 4, which will be better described subsequently, thesecond analog/digital conversion means E4, which generates the commandof the temporal sequence of currents.

Notations

In a preferred embodiment, Ne=Nc=3 will be taken.

The total field B_(TE), three-component vector (pseudo vector), existingat the center of the sensor is the sum of the following inductions:{right arrow over (B)} _(TE) ={right arrow over (B)} _(EU) +{right arrowover (B)} _(EMI) +{right arrow over (B)} _(ECI) +{right arrow over (B)}_(FMI) +{right arrow over (B)} _(T)  [1]with{right arrow over (B)} _(EU) ={right arrow over (B)} _(EU1) +{rightarrow over (B)} _(EU2) +{right arrow over (B)} _(EU3)  [2]

where {right arrow over (B)}_(EUj) is the induction expressed in thetransmitter mark, and emitted by the transmission axis j (j=1 to 3) atthe center of the sensor C-1. It is presumed in the equation [2] thatthe emission is simultaneous on the three transmission axes E1, sinceB_(EU) is the sum of the three inductions.

B_(EMI) is the vector of the induction radiated in the environment, forexample, generated by the currents circulating in the electricalequipment, by the on-board generators, by the 50-60 Hz sector, etc. Thesame can be modelled by the sum of periodic fields B_(SC) not correlatedwith the B_(EUj) and fields B_(R), which are EMI signals, thecharacteristics of which are presumed random because they cannot berepresented by deterministic signals of known or estimatedcharacteristics.{right arrow over (B)} _(RM)(t _(k))={right arrow over (B)} _(SC)+{right arrow over (B)} _(R)  [3]

B_(ECI) is the induction vector at the center of the sensor, created bythe Eddy currents in the conductors situated in the environment of theP/O system, the same produced by the magnetic field emitted by thetransmitting antenna at the location where the conductors are found.

B_(FMI) is the induction vector at the center of the sensor, created bythe magnetization of ferromagnetic materials situated in the environmentof the P/O system.

B_(T) is the induction of the earth's magnetic field.

It should be noted that, according to FIG. 4, the induction B_(EU) isthe useful signal very strongly correlated with the emitted currentsand, more specifically, B_(EU) is linearly dependent on the measurementsXu of the fields emitted by the three axes El and measured according toE-3, the inductions B_(ECI) and B_(FMI) are also strongly correlatedwith the emitted field Xu.

One of the aims of the disclosure is to eliminate by filtering all ofthe inductions so as to only keep the measured vector, the model ofwhich is expressed by B_(CU)=[R_(c/e)]^(t) (B_(Eu1)+B_(Eu2) B_(Eu3))where B_(EU1), B_(EU2), B_(EU3) are the three-component vectors of thefield emitted and received at the center of the sensor (expressed in themark of the transmitter) and R_(C/E) is the rotation of the sensor markrelative to the mark of the transmitter. Demultiplexing of thetransmission channels is carried out (recognition of the portion of thesignals that comes from the transmission channel j=1 to 3), i.e., todetermine the components Bc₁, Bc₂, Bc₃ of the sensor C-1 coming from theemission of the axes 1, 2 and 3 of the transmitter E-1 in order to formthe 3×3 matrix: [Bcu]=[Bc₁|Bc₂|Bc₃]. The method for computing therotation of the sensor is obtained in a known manner (U.S. Pat. No.4,287,809 to Egli): knowing B_(cu), an estimation of B_(EU) is deducedby using an induction model in free space (without disturbances):R_(C/E)=B_(C) B_(EU) ⁻¹.

From the matrix [R_(c/e)], the Euler angles or the quaternion Q^(EM),which are two representations of the attitude of the object M, are takenin a known manner.

The static and dynamic accuracy performances are obviously increasingwith the S/N ratio. The increase of the S/N ratio sought is obtained intwo obvious and complementary manners: increase the power (or theamplitude) of the useful signal in particular in low frequency andjointly reduce the power of the noise by filtering.

Transmitting Assembly E

A first aim of the disclosure is the assembly E, which includesaccording to FIG. 4:

-   -   a second transmitting sub-assembly consisting of Ne means of        injection E-2 of predetermined currents through the j coils E-1,        j=1 to Ne of the first assembly E in order to generate a        predetermined induction flux Fj(t) as a function of the time        according to the characteristics specific to each axis j of the        coils; a preferred embodiment consists of including in the        interior volume of the j coils E-1 a highly permeable magnetic        material of the type ferrite bar or μmetal wires or of        ferromagnetic alloy such as VITROVAC® or PERMALLOY®, etc. The        magnetic material, as will be subsequently described, makes it        possible to multiply the magnetic induction under certain        conditions of form, which will be discussed.    -   a third sub-assembly E-3 of the first transmitting assembly E        consisting of means of measurement of the electromotive force        due to the induction flux Fj(t) relative to each axis of the Ne        transmitting coils E-1, the assembly E-3 including one magnetic        sensor for each transmission axis, which measures the flux        emitted, and one electronic for adapting the signals E-3-2. Any        magnetic induction sensor (fluxgate, controlled fluxmeter, Hall        effect sensor, AMR, GMR, TMR) may also be suitable for measuring        the fields. However, a preferred embodiment consists of winding        the turns concentrically relative to the coils E-1 to form a        simple fluxmeter sensor. A voltage amplifier E-3-2, preferably        comprising a pure incorporation of the signals such that the        magnitudes X_(Uj) are homogeneous to a magnetic induction,        produces the interface on one hand with the ADC acquisition        system 4-1 of the processor 4, on the other hand with the block        E-2, which constitutes the current control device of the coils        E-1. The input or setpoint of the control E-2 is the        three-component signal V_(IC) provided by the block E-4, which        is the generator of the sequence of Ne predetermined cyclical        currents of periodicity T_(obs). The block may be autonomous        (memory equipped with a sequencer and containing the sequences        of setpoint values of the currents) or even, in a preferred        embodiment indicated in FIG. 4, incorporated into the processor        4. The values of the sequence are preferably random binary        values, the sequence is known as PRBS for Pseudo-Random Binary        Sequence, the embodiment and properties of which are known by        the person skilled in the art. The binary values of the sequence        between −V_(IC) and +V_(IC) volts are provided with the        recurrence of T_(e)=T_(obs)/N_(obs) where N_(obs) is the        characteristic number of values of the sequence generated. The        same are deterministic signals over the duration T_(obs) of        constant spectral density as a random noise known as white, over        the range of frequencies between 1/T_(obs) and 1/T_(e). FIG. 5        shows for one of the axes j the transfer functions of blocks        E-1, E-2, E-3 from FIG. 4, which form part of the control of the        emitted magnetic induction. The signals Xu_(j) constituting the        measurement of the magnetic inductions emitted by the axes E-1        are subtracted from the corresponding signals V_(IC) to form the        error c of the control, the same being processed by a corrector        network E-2-1, which compensates in a known manner the transfer        function of the current amplifier and mainly the time constant T        of the windings with magnetically permeable core E-1, the time        constant T being close to the ratio between the total inductance        L and the resistance r_(b) of the coil. The transfer function of        the current generator block E-2-2 takes into account the        characteristics of the winding. The magnetic field H_(I)        produced by the current is proportional to the number of turns        per unit of length n with a coefficient of proportionality        K_(b), which depends in a known manner on the geometrical shape        of the winding. The magnetization of the core is based on the        sum of H_(I) and the disturbing magnetic fields present in the        environment H_(EMI). The magnetic induction B_(E) produced in a        point of the space outside of the windings by the currents and        the core may be written B_(E)=μ_(eff)·(H_(I)+H_(EMI)), where        μ_(eff) effective permeability represents the proportionality        term between the magnetic excitation field H₁ and the output        magnetic induction, the magnetic field H_(I) is proportional to        n*I, “n” being the number of turns per unit of length and I is        the intensity of the current circulating in the turns of the        transmitting coil E-1. It is known that the coefficient μ_(eff)        is based on the relative permeability of the magnetic material,        of the geometrical shape of the cores, the shape determining the        demagnetizing field within the material, of the ratio between        the interior volume of the coil and the volume of the material,        but also losses by Eddy currents. The means for obtaining the        values of μ_(eff)>>100 will subsequently be indicated. In the        control, the detector of the electromotive force E-3-1        previously described has a transfer function K_(BV)*p        (derivation with induction conversion variation        ΔB_(E)/Volt=K_(BV) into Tesla per Volt). The block E-3-2 carries        out a pure incorporation of gain K_(CR) to obtain a homogeneous        output with the setpoint V_(ic).

The main object of the control is to cancel out the EMI magnetic fieldspresent in the environment, which are added to the exciter fieldproportional to n*I_(j), where I_(j) is the current relative to thewinding j, but also to linearize the coefficient μ_(eff) because it isknown that the magnetization of magnetic materials has a non-linearmagnetization curve with saturation for the strong excitations.

From FIG. 5, it is easily shown that the output B_(E) is the following:

$B_{E} = {{\frac{G \cdot F}{1 + {G \cdot F}}\frac{V_{ic}}{F}} + {\frac{\mu_{eff}}{G \cdot F}H_{EMI}}}$with $F = \frac{\Delta\; V_{IC}}{\Delta\; B_{E}}$ and${G = {K_{G}\frac{K_{A}}{R}{K_{b} \cdot n \cdot \mu_{eff}}\frac{1 + {\hat{T}p}}{1 + {Tp}}}};$

μ_(eff) is the effective permeability if in addition in the useful band:GF>>1

$\begin{matrix}{{B_{E} \approx {\frac{V_{ic}}{F} + {\frac{\mu_{eff}}{\mu_{0} \cdot G \cdot F}B_{EMI}}}} = {\frac{V_{ic}}{F} + {\frac{\mu_{r\_ eff}}{G \cdot F}B_{EMI}}}} & \lbrack 4\rbrack\end{matrix}$

with μ_(r) _(_) _(eff) effective relative permeability

where B_(EC) is the induction produced at the center of the core andμ_(r) _(_) _(eff) the effective relative permeability. Thesignal-to-noise ratio in the coreless and control-less configuration is

$\frac{V_{ic}}{F}/{B_{EMI}.}$With core for E-1 and control E-2, it is seen that the signal-to-noiseratio is

${\frac{V_{ic}}{F}/\frac{\mu_{r\_ eff}}{G \cdot F}}{B_{EMI}.}$To keep the same signal-to-noise ratio while keeping the same order ofmagnitude for B_(E) in output, it is, therefore, necessary thatG·F≥μ_(r) _(_) _(eff). The relation defines the minimum gain of thecontrol chain. The corrector network of the shifted proportional typeK_(G) (1+{circumflex over (T)}p) must be adjusted according to the rulesknown for ensuring the stability of the control. It is also possible toproduce a PID according to the techniques taught automatically. Anotherinteresting aspect of the disclosure is the linearization of the fieldemitted by the control. As μ_(r) _(_) _(eff) is a highly non-linearfunction, the hamionics B_(harmo) appear as output of E-1 in FIG. 5. Ifthe output is expressed according to the inputs V_(ic), B_(EMI) andB_(harmo), the following is obtained:

$\begin{matrix}{{B_{E} = {\frac{G \cdot F}{1 + {G \cdot F}}\left( {\frac{V_{ic}}{F} + \frac{B_{harmo}}{G \cdot F} + {\frac{\mu_{r\_ eff}}{G \cdot F}B_{EMI}}} \right)}}{B_{E} \approx {\frac{1}{F}\left( {V_{ic} + \frac{B_{harmo}}{G} + {\frac{\mu_{r\_ eff}}{G}B_{EMI}}} \right)}}} & \lbrack 5\rbrack\end{matrix}$

It is observed that if G*F>>1, the amplitudes of the harmonics aredivided by the gain of the direct chain G. That said, as will behighlighted in the paragraph dealing with the modelling and filtering,the fact of measuring X_(uj) and of using reference signals of theinduction emitted in the model of signals received, makes the filteringdevice insensitive to harmonics, which is a fundamental advantagerelative to existing systems for which the measurement of the current inE1.1, E1.2, E1.3 is no longer the image of the induction emittedfollowing the appearance of harmonics.

As said previously, one of the aspects of the disclosure consists ofproducing a core in order to obtain an effective relative permeabilityμ_(r) _(_) _(eff) of a few hundreds of units. The existence of cores offerrite or of shims made of ferromagnetic alloy exists in a number ofapplications. The latter used, for example, in transformers, must belaminated to reduce the Eddy currents, which counter the magnetizationand cause losses. Ferrite, much more conductive than ferromagneticalloys, makes it possible to use cores with uniform density of thematter obtained by sintering. In general, the cores are spherical orcubic (or even parallelepiped) according to FIG. 6. The magnetization ofthe permeable matter of the cores subject to an excitation of magneticfield is a complex phenomenon because of developing a demagnetizingfield that counters the excitation field. The demagnetization field isoften explained by the creation of dummy magnetic fields on the surfaceof the volumes of ferromagnetic matter. Therefore, it is simplyexplained that the demagnetizing field is closely linked to the geometryof the volume of the core and to the magnetization. The demagnetizingfield can only be computed for simple examples (sphere, ellipsoids,cylinders). In the general case, approximations are made. Thus, for asphere of material of infinite relative permeability μ_(r), it is shown(c.f. J. D. Jackson, Classical Electrodynamics, ed. Wiley) that theeffective relative permeability μ_(r) _(_) _(eff) is at a maximum ofthree. For a cube, the value is of the same order of magnitude. Withcubic or spherical cores, very high gains cannot be expected. It isknown that for elongated cylinder-shaped bars of diameter D and lengthL, the demagnetizing field H_(D) at the center is −0.5*(D/L)²*M, i.e.,Hd=−δ*M where the magnetization M is of the type M=(μ_(R)−1)H, H beingthe magnetic field present within the material after the magnetization,with the relation H=H₀-H_(D), H₀ being the external magnetic excitationfield and δ is the demagnetizing factor. Close to the edges, thedemagnetizing field is M/2.

From the preceding relations, a formula of the induction is deduced, forthe ellipsoids of which the magnetization is uniform,

$\begin{matrix}{{B = {{\mu_{0} \cdot \frac{\mu_{R}}{1 + {\left( {\mu_{R} - 1} \right) \cdot \delta}}}H_{0}}}{{and}\mspace{14mu}{if}}{{\mu_{R}\operatorname{>>}1},{B = {\frac{\mu_{R}}{1 + {\mu_{R} \cdot \delta}}{B_{0}.}}}}} & \lbrack 6\rbrack\end{matrix}$

In general, μ_(R)·δ>>1, therefore,

$B = {\frac{B_{0}}{\delta}.}$

Using the preceding example of the elongated bar, this gives

$B = {{2 \cdot \left( \frac{L}{D} \right)^{2} \cdot B_{0}} = {\mu_{r} \cdot {B_{0}.}}}$The relation is only approximate, the value of μ_(r) is, in general,lower because the magnetization is not uniform. Experimentally, theexponent is between one and two, but an increase in the induction in theorder of μ_(r) is indeed observed in the volume of the material, butalso on the outside.

Therefore, the disclosure consists of an arrangement of permeable barsof L/D ratio chosen so that the gain in induction μ_(r) _(_)_(eff)=α·μ_(r) is higher than ten. The coefficient α, lower than theunit, takes into account a plurality of factors, in particular:

-   -   the volume of magnetized material parallel with each axis of the        coils, with each axis having to have the same volume and the        volume of each one is a third of the total volume available.    -   the manner in which they are wound, the turns producing the        excitation field H₀.    -   the Eddy currents induced by H₀.

According to the disclosure, to optimize the coefficient α, very thinbars of permeable material are used, for example, wires of μmetal,PERMALLOY® or VITROVAC® electrically isolated in advance, storedaccording to Panel 7-1 of FIG. 7 in a tube of material resistant to heattreatments (silica, ceramic).

Thus, according to the at least two non-parallel transmission axes, thebars are grouped (Panel 7-2 of FIG. 7) to form a block of square section(Panel 7-3 of FIG. 7) or cylinder shape (Panel 7-4 of FIG. 7) comprisinga large number of bars. The blocks of Panels 7-3 and 7-4 of FIG. 7 arearranged so as to form three volumes of orthogonal magnetizationmaterials and having a symmetry relative to the center common to thethree axes.

FIG. 8A shows how the assembled blocks of Panels 7-3 or 7-4 of FIG. 7can be used: three windings are produced around three identical blocksthat are then assembled mechanically to form three substantiallyperpendicular axes. The three coils are not concentric, which posessignificant difficulties for finding the position of the three-axissensor attached to the object the position and orientation of which isto be found. Therefore, preference will be given to concentrictransmitting blocks according to FIGS. 8B and 9. In FIG. 8B, preferableconfigurations of blocks are shown so that there is a center of symmetryof the three magnetized volumes and that each axis has a magnetic momentof similar value. FIG. 9 has two projection views of a preferred devicethat is a generalization of the preceding blocks: a plurality of blocksof type 2-3 are interlinked according to the three directions such thatthere is the best symmetry relative to a central point. According toFIG. 9, a cubic block is obtained on which three substantiallyorthogonal windings are arranged through which will pass the currentsinjected by the electronic circuits. So that the magnetic inductionvector behaves in the space according to the equations of the dipole, inaccordance with embodiments of the present disclosure, a block isproduced, the external surface of which is similar to a sphere, byhaving the blocks shown in Panels 7-3 or 7-4 of FIG. 7 of shorter lengthwhen moving further away from the center.

A device consisting of producing three concentric spherical coilsinstead of the concentric cubic coils as shown in FIG. 9, andintroducing the same overlap of blocks of the type shown in Panels 7-3or 7-4 of FIG. 7 in the volume of the inner coil remains within thefield of the invention.

Another aspect of the disclosure concerns the control at zero of thequasi-static magnetization produced by quasi-static disturbances, suchas, for example, the earth's magnetic field. To avoid the saturation ofthe bars of blocks shown in Panels 7-3 or 7-4 of FIG. 7 in the presenceof a continuous or quasi-continuous magnetization, the symmetry of thecurrents circulating in the coils is detected. FIG. 10A shows theoperating principle: when a static or quasi-static field Hext is presentin the environment, the projection H_(D) thereof according to thetransmission axis E.1 offsets the point of operation of the alternatingexcitation field H_(i) produced by the coils according to the diagram inFIG. 10B. When the offset H_(D) is zero, the difference between the peakvalues I₀ ⁺ and I₀ ⁻ is zero. If H_(D) is not zero, the differencebetween the peak values I_(D) ⁺ and I_(D) ⁻ is not zero. This is due tothe non-linearity of the magnetization curve of the ferromagneticmaterials that modifies the inductance of the coil L depending on theexcitation H sum of the external field H_(ext) and of the excitationH_(i) created by the current of the coils knowing that L=μ_(r)(H)×L₀with L₀ inductance of the coreless coil. Exploitation of the impedancevariation that deforms the current is carried out by the detection ofthe symmetry of the current circulating in the coil. The current throughthe resistance R_(JMj) is measured at point E.1.j, j=1 to 3, by theimpedance adapter amplifier E.5.2, the output voltage of which passesthrough a double peak detector E.5.1, which in a known manner detectsthe positive peak value I_(D) ⁺ and the negative peak value I_(D) ⁻.Then, the difference I_(D) ⁺−I_(D) ⁻ is filtered by a filter RC of thefirst conventional order, the cut-off frequency of which is a few Hertz.The output V_(CRJ) of E.5.1 is then added to V_(lcj), with the signadapted according to the direction of winding so as to cancel out thefield offset H_(D). The symmetry of the current could also be detectedby the creation of even harmonics of the current knowing that thesymmetrical excitation Hi only has odd harmonics.

A. The on-Board Processor 4:

The computing processor is coupled with the three measurement assembliesC-1, C-2, C-3, previously described, in order to first produce atdiscrete times t_(k)=k*Te the acquisition of signals, on one hand, byanalog/digital conversion of the second receiving assembly C-1 as wellas of the third sub-assembly E.3.1 of the first transmitting assembly E,on the other hand, by digital serial links of the third assembly foracquiring angular velocities C.3.1 at the frequency F_(EG) as well asthe angles of attitude of a second object M relative to the absolutefixed mark delivered by C.3.2. Second, to generate and producedigital/analog conversions by the block E.4 for providing the setpointsof the control of predetermined currents in the first transmittingassembly E. Third, to produce the computations of a firstposition/orientation from a complete model of the measured inductions,the variables of which are developed from the signals acquired and someparameters of which, identified by optimum filtering, represent theterms proportional to a dipolar or multipolar field model of which theposition and orientation of the block C-1 are extracted. The block 4.3,receives, for example, from a conventional digital serial link thatcommunicates with the inertial system of the platform, the informationdated relative to the specific clock of processor 4 is constituted. Ifnecessary, this makes it possible to temporally reset the attitudes ofthe platform. The block also receives the serial type digitalinformation of the MEMS inertial sensor C-3-1.

B. Method for Extracting the Noise Reference:

If the equation [1] is used,{right arrow over (B)} _(TE) ={right arrow over (B)} _(EU) +{right arrowover (B)} _(EMI) +{right arrow over (B)} _(ECI) +{right arrow over (B)}_(FMI) +{right arrow over (B)} _(T)  [7]the useful signal {right arrow over (B)}_(EU) is linearly dependent onthe signals emitted by the transmitter block E. According to FIG. 4, thefields emitted by the axes El are measured by the block E3 previouslydescribed as the output of which is Xu_(j). In other words, Xu_(j) isthe image of the magnetic field emitted by the axis j regardless of thenon-linear amplification function provided by the magnetic cores. It canbe noted that the sum of the ECI and FMI noises noted B_(PCU)={rightarrow over (B)}_(ECI)+{right arrow over (B)}_(FMI) (PCU for disturbancescorrelated with U) are the noises correlated with Xu. The earth'smagnetic field is presumed to be filtered by a known conventional filternot forming part of the invention. Concerning the EMI additive noises,for one particular embodiment of the invention, same are measured by theblock C-2: as indicated in FIG. 3A, the block C-2 is fixed in theplatform P, including a plurality of sensors installed in points suchthat i) the field emitted by the assembly E-1 is quasi zero or at thevery least much lower than the point, contained in the volume of motionof the sensor, where C-1 of the mobile assembly M is situated, ii) thedisturbance fields statistically not correlated with the fields emittedby E-1 and existing in the center of the sensor C-1 are very stronglycorrelated with said fields measured by C-2. The above notions aresubsequently specified.

Consequently, it will be considered that the additive noise {right arrowover (B)}_(EMI) measured in Nb points of the environment, by definitionnot correlated with the fields emitted estimated Xu has been noted{right arrow over (B)} _(RM)(t _(k))={right arrow over (B)} _(SC)+{right arrow over (B)} _(R)  [8]

The signal {right arrow over (B)}_(RM) (t_(k)) is shown in FIG. 4 by theanalog signals Sb, which are output from the block C-2 and which aredigitalized as the signals Xu_(j) and Sc_(i), j=1 to Ne, i=1 to Nc.

In some environments, such as, for example, airplanes, the noise B_(EMI)is lower than in helicopter environments and, in particular, the noiseB_(R) is very low. In such a type of environment, the noise may have tobe extracted instead of being measured. The definition of the block 4.4,therefore, enables a method for extracting the reference noiseB_(RM)(t_(k)) in two different manners:

i. First Method:

Either an extraction directly from the signal Sc (obtained by theacquisition of the signal provided by the first measurement assemblyC-1). In this case, a choice is made by the processor in the block 4.4depending on the nature of the magnetic noise. The choice ensues from aninitial analysis of the magnetic noise of the environment when poweredor at the request of the user. For example, when powering on, in theabsence of signals emitted by the transmitting antenna, if the meanpower density values of the measured signals are harmonic and ofacceptable frequency stability (variation of 10% to 20% maximum of themean frequency) and less than the mean power density level of thesignals due to the emission of the transmitting antenna when same emits,the choice is made. The choice may also be made by the user followingthe accumulation of the experience that has been obtained from theenvironment or any other means. The choice requires the transmittingpower to be zero during a period of time T_(off), the period T_(off)being interlinked between at least one transmission period of timeT_(obs) at power not zero, with T_(off)<T_(obs)/2. Two examples aregiven in FIG. 11. Over the period T_(OFF) the stationary disturbancesignals (low variability over T_(0BS)) are identified in the same manneras same that will be described for the extraction of the same signals onthe signal Sb. The model of these signals B_(sc) or B_(ESC) (the letter_(E) indicates that the vector is expressed in the transmitter mark)

$\begin{matrix}{{B_{SC}\left( {i_{c},t_{k}} \right)} = {{\sum\limits_{k_{sc} = 1}^{N_{sc}}{{{\hat{C}}_{SC}^{re}\left( {i_{c},k_{sc}} \right)} \cdot {\cos\left( {\omega_{k_{sc}}t_{k}} \right)}}} + {{{\hat{C}}_{SC}^{im}\left( {i_{c},k_{sc}} \right)} \cdot {\sin\left( {\omega_{k_{sc}}t_{k}} \right)}}}} & \lbrack 9\rbrack\end{matrix}$the frequencies ω_(k) _(sc) of which are estimated (by methods of theFFT type or preferably by methods of the High Resolution type). Thecoefficients are identified up to T_(off).

As another example, two periods T_(OFF) can be considered according toFIG. 11 outlining the period of transmission T_(ON) to produce a linearinterpolation of the parameters Ĉ_(SC) ^(re) (i_(c), k_(sc)) and Ĉ_(SC)^(im) (i_(c), k_(sc)). The output information is therefore offset fromT_(ON), but the time may be very short if a HR (High Resolution) methodis used to identify the equation [9].

The independent variables X_(C)(t_(k))=cos(ω_(k) _(sc) (t_(k))) andX_(S)(t_(k))=sin(ω_(k) _(sc) (t_(k))) are deduced therefrom during theperiod T_(ON). The variables can be grouped under the term of X_(sc),which becomes a matrix [N_(obs), 2] where N_(obs) is the number ofsamples acquired during T_(ON): N_(obs)=T_(ON)*Fe. The variables areadded to the variables Xu₁ to form a model relatively linear toindependent variables X_(UJ), X_(sc). Each component i_(c) of the sensorC-1 may be written as follows, if B_(R) is negligible:B _(E) ={circumflex over (B)} _(EC)(i _(c) ,t _(k))+{circumflex over(B)} _(RM)(i _(c) ,t _(k))  [10]

with

$\begin{matrix}{{{\overset{\Cap}{B}}_{EC}\left( {i_{c},t_{k}} \right)} = {\sum\limits_{j = 1}^{N_{e}}{\sum\limits_{k_{i_{c}} = 0}^{N_{i_{c}}}{{{\hat{A}}_{C}\left( {i_{c},j,k_{i_{c}}} \right)} \cdot {X_{C}\left( {i_{c},j,k_{i_{c}}} \right)}}}}} & & \lbrack 11\rbrack\end{matrix}$

where X_(C) (j, k_(i) _(c) , t_(k))=X_(U) _(j) (t_(k)−k_(i) _(c) Te)[10] is written:

$\begin{matrix}{B_{E} = {{\sum\limits_{j = 1}^{N_{e}}{\sum\limits_{k_{i_{c}} = 0}^{N_{i_{c}}}{{{\hat{A}}_{C}\left( {i_{c},j,k_{i_{c}}} \right)} \cdot {X_{C}\left( {i_{c},j,k_{i_{c}}} \right)}}}} + {\sum\limits_{k_{sc} = 1}^{N_{sc}}{{{\hat{C}}_{SC}^{re}\left( {i_{c},k_{sc}} \right)} \cdot {\cos\left( {\omega_{k_{sc}}t_{k}} \right)}}} + {{{\hat{C}}_{SC}^{im}\left( {i_{c},k_{sc}} \right)} \cdot {\sin\left( {\omega_{k_{sc}}t_{k}} \right)}}}} & \left\lbrack {10\text{-}{bis}} \right\rbrack\end{matrix}$

It is noted that X_(C) (j, k_(i) _(c) , t_(k)) are the values offsetover time of the fields emitted by the transmitter on each axis j andfor each component i_(c) of the sensor of the block C-1. In a way, theestimator is a transversal filter that is justified by the fact that theECI and FMI disturbances may be considered as the output of filterssubstantially of the first order of which the input are the signalsX_(Uj)(t_(k)).

The indexes K_(ic) are relative to the delays of the independentvariables of the model and range from 0 to Ni_(c), the latter indexN_(ic) being defined strictly necessary in order to minimize theresidual error. The offset terms of K_(ic) form a transversal filter.B_(RM) is written in the form of a development of complex variables:

$\begin{matrix}{{{{\hat{B}}_{RM}\left( {i_{c},t_{k}} \right)} \cong {{\hat{B}}_{SC}\left( {i_{c},t_{k}} \right)}} = {\sum\limits_{k_{sc} = 1}^{N_{sc}}{{{\hat{C}}_{SC}\left( {i_{c},k_{sc}} \right)} \cdot {X_{sc}\left( t_{k} \right)}}}} & \lbrack 12\rbrack\end{matrix}$

Equations [11] and [12] are linear relative to the parameters to beestimated.

If a model was produced for X_(sc)(t_(k)) of the same type as [11],i.e., a development sum of the type [12] for each variableX_(sc)(t_(k)−k_(sc)·T_(e)), this would remain within the field of theinvention. The same would apply if the complex parameters Ĉ_(SC) (i_(c),k_(sc)) were no longer constant but depended on the time in the form ofa polynomial of the time

${{\hat{C}}_{SC}\left( {i_{c},k_{sc},t_{k}} \right)} = {\sum\limits_{{io} = 0}^{{io} = N_{io}}{{C_{io}\left( {i_{c},k_{sc}} \right)} \cdot {t_{k}^{io}.}}}$For the temporal model, the values of the terms C_(io), (i_(c), k_(sc))are computed by developing same in [12]. Any type of different temporalmodel no longer comprised of temporal polynomial but of sums offunctions of the time of exponential type e^(a·t) or e^(i·b·t) (complexperiodic function ⇔i²=−1) remains within the field of the invention.

The parameters of the model are determined by a conventional method ofleast squares (MSE) or an equivalent recursive method (LMS, RLS). Theestimation of the parameters relative to the variables Xu_(j) may berefined by subtracting the term {circumflex over (B)}_(SC)(i_(c), t_(k))estimated at the signal Ŝc(i_(c), t_(k)). The new estimation makes itpossible to estimate the correlated terms with better accuracy after oneor two iterations. The reference noise {circumflex over (B)}_(RM) is inthis case the signal {circumflex over (B)}_(sc) estimated in thepreceding iteration.

ii. Second Method:

The continuous measurement of disturbance signals by S_(b) may beessential in the presence of very strong harmonic signals ofnon-constant amplitudes and frequencies up to T_(obs) but also in thepresence of non-stationary deterministic disturbances or randomdisturbances, i.e., an estimation of the signals radiated by themeasurement of the signals S_(b). As described and illustrated in FIG.4, the signal noted S_(b) consists of signals coming from at least onemagnetic sensor of one to three orthogonal axes for measuring themagnetic fields between the continuous and a few KHz (fluxgate sensor,fluxmeter, AMR, GMR, TMR, etc.), the sensors being attached to thesecond object in at least Nb points measure the vector sum of themagnetic inductions present in the Nb points of the environment,sufficiently far enough away from the first transmitting assembly sothat the assembly constitutes a noise reference B_(RM)(t_(k)) bypreferentially measuring the magnetic inductions independent of theinductions generated by the first transmitting assembly E1. Measurementsmay be produced without interruption (T_(off)=0).

The measurements of the additive noise B_(EMI) are identified by theoutput signals S_(b) of the block C-2 of FIG. 4. In a particularembodiment, in order to facilitate the drafting, Nb=1 will be taken andit will be considered that the measurement of a single component issufficient. The measurement of {right arrow over (B)}_(RM) (t_(k))according to a particular direction will be noted to be considered as asignal very strongly correlated with B_(EMI). In the ideal situation,the measured noise reference B_(RM) contains no signal correlated toXu_(j), j=1 to 3. In practice, it is very difficult to arrange sensorsC-2 at locations such that no component correlated with X_(U) exists,including and in particular the signals B_(ECI) and B_(FMI). Therefore,the signal for measuring the noise S_(b) consisting of the samecomponents as the signal S_(c) must be considered. Therefore, the sameproblem arises as in i), i.e., that the various components of the signalS_(b) must be identified that are written as follows:B _(C2) =B _(RU) +B _(RM)  [13-a]with B _(RU) =B _(U) +B _(PCU)  [13-b]

where B_(U) is linearly dependent on X_(Uj)(t_(k)), B_(PCU) is linearlydependent on X_(Uj) (t−k·Te) andB _(RM) =B _(SC) +B _(R)  [14]

is the term not correlated with X_(Uj).

B_(RM) is not negligible as in i) and this consists of extracting from[13-a] the portion B_(RM). As in the case i), all of the terms of themodel must be identified to prevent biasing the estimation of theparameters of the model. However, the random signal B_(R) is in generalweaker than B_(SC) and B_(cu), and the identification may be performedover longer times insofar as the sensors of C-2 are immobile. It canalso be considered that, since the transmitter and the sensor(s) of theblock C-2 are fixed on the same structure, the identification of theparameters of the model [14] may be carried out once for all, or indeedat the start of use of the system during an initialization phase ofsufficient duration in order to enable very good accuracy in theestimation of the parameters following filtering of the terms of [14],which are not correlated with [14]. The identification is exactly thesame as that described in [10], [11], [12]. The parameters of [14] are,therefore, stored in memory for the computation of {circumflex over(B)}_(CU). The principle of extraction of B_(RM) consists of writing:{circumflex over (B)} _(RM) =B _(C2) −{circumflex over (B)}_(RU)  [16-a]

where {circumflex over (B)}_(RU) are the estimates of the signalscorrelated with Xu_(j).

After the identification of the model of the type:

$B_{E} = {{\sum\limits_{j = 1}^{N_{e}}{\sum\limits_{k_{i_{c}} = 0}^{N_{i_{c}}}{{{\hat{A}}_{C}\left( {i_{c},j,k_{i_{c}}} \right)} \cdot {X_{C}\left( {i_{c},j,k_{i_{c}}} \right)}}}} + {\sum\limits_{k_{sc} = 1}^{N_{sc}}{{{\hat{C}}_{SC}^{re}\left( {i_{c},k_{sc}} \right)} \cdot {\cos\left( {\omega_{k_{sc}}t_{k}} \right)}}} + {{{\hat{C}}_{SC}^{im}\left( {i_{c},k_{sc}} \right)} \cdot {\sin\left( {\omega_{k_{sc}}t_{k}} \right)}}}$

All of the terms of the signals correlated with Xu_(j) are extractedtherefrom to form the signal {circumflex over (B)}_(RU):

$\begin{matrix}{{{\overset{\Cap}{B}}_{RU}\left( {i_{c},t_{k}} \right)} = {\sum\limits_{j = 1}^{N_{e}}{\sum\limits_{k_{b} = 0}^{N_{b}}{{{\overset{\Cap}{A}}_{BRC}\left( {i_{c},j,k_{b}} \right)} \cdot {X_{C}\left( {i_{c},j,k_{b}} \right)}_{\;}}}}} & \left\lbrack {16\text{-}b} \right\rbrack\end{matrix}$

{circumflex over (B)}_(RM) of [16-a] is, therefore, the estimate of thenoise not correlated with the emitted fields.

It is, therefore, noted that when there is emission of signals by E-1,in the two embodiments i) and ii), previously described, the same modelshould be identified on the measurements Sc (coming from the block C-1)or S_(b) (coming from the block C-2).

The model of the signal to be identified within the framework of thesecond embodiment of the invention for which a measurement of the EMInoise is taken, and of which only the BRM noise is extracted, is,therefore, produced.

The model of B_(c) is developed which is the field measured by thesensor C-1:{right arrow over (B)} _(C) =R _(C/E) ^(t)({right arrow over (B)} _(U/E)+{right arrow over (B)} _(CU/E)+{circumflex over ({right arrow over(B)})}_(RM/E))  [17]

In the index _(U/E), _(E) indicates that the vector is expressed in themark of the transmitter (the index is sometimes omitted bysimplifications knowing that the context indicates in which mark thefields are expressed), _(U) indicates that this is the portion of thefield linearly dependent on the fields emitted by the transmitter X_(U).The index C_(U) indicates that {right arrow over (B)}_(CU/E)≡{rightarrow over (B)}_(ECI)+{right arrow over (B)}_(FMI) represents the vectorof the disturbances correlated with the vector X_(U). {right arrow over(B)}_(CU/E) could be modelled by the convolution of {right arrow over(B)}_(U/E) by the impulse response of the complex filter existingbetween the two magnitudes. {circumflex over ({right arrow over(B)})}_(RM/E) has the same meaning as in [13] and [15], it is the noisepresent in the environment not correlated with the emitted fields.

B_(T), which is overlooked, is presumed to be filtered by a conventionaldigital filter known by the person skilled in the art. The three modelsare developed linearly relative to the parameters to be identified, forexample, by a conventional square error minimization method. When thecoefficients are determined, the nine terms (three terms due to eachtransmission channel for each component of the triaxial sensor C-1) areextracted relative to X_(U)(t_(k)) components of the matrix noted “A,”which will be better defined subsequently. The fundamental interest ofthe complete modelling of the signals received by the sensor C-1 lies inthe fact that the nine parameters of A are even less biased if theindependent variables of the model more accurately represent thephysical phenomena.

The following three models of [17] are developed: Model {right arrowover (B)}_(U/E), Model {right arrow over (B)}_(CU/E), Model {right arrowover (B)}_(RM/E):

Model {right arrow over (B)}_(U/E):

Consequently, it is considered that the sensor C-1 has been corrected ofthe errors thereof according to known methods: the functions of gaincorrection, misalignment, etc., are applied. Presuming that the distancebetween the sensor C-1 and transmitter is at least three times thelargest dimension of the transmitter, it is therefore written in a knownmanner that the model is of dipolar type and is written

$\begin{matrix}{{B_{C}(t)} = {{{{\left\lbrack {R_{c/e}(t)} \right\rbrack^{t}\;\lbrack P\rbrack}^{t}\lbrack H\rbrack}\;\lbrack P\rbrack}\;\left( {{M_{1}{f_{1}(t)}} + {M_{2}{f_{2}(t)}} + {M_{3}{f_{3}(t)}}} \right)}} & \lbrack 18\rbrack \\{H = \frac{\begin{bmatrix}2 & 0 & 0 \\0 & {- 1} & 0 \\0 & 0 & {- 1}\end{bmatrix}}{D_{C/E}^{3}}} & \lbrack 19\rbrack\end{matrix}$

D_(C/E) is the distance between the center 0 _(C) of the sensor C-1 andthe center of the transmitter 0 _(e):O _(E) {right arrow over (O)} _(C) ≙D _(C/E) ·{right arrow over(u)},  [19-bis]

D_(C/E) is variable as a function of time, like the rotationR_(C/E)(t′,·{right arrow over (u)}: unit vector of O_(E){right arrowover (O)}_(C) expressed in the reference mark of the transmitter R_(E)that is mechanically defined in a known manner by the person skilled inthe art relative to the mark of the platform R_(p) according to FIG. 2.

P is the transfer matrix between the mark of the transmitter and themark ({right arrow over (u)}, {right arrow over (v)}, {right arrow over(w)}) with {right arrow over (w)}={right arrow over (u)}_(M)^{rightarrow over (u)} and {right arrow over (v)}={right arrow over (w)}^{rightarrow over (u)} and known as the radial mark, where {right arrow over(u)}_(M) is the unit vector of a transmission axis. It is also shownthat, for example:

$\begin{matrix}{{{{{{{{If}\mspace{14mu}\overset{\rightarrow}{u}} =}}\begin{matrix}x & \; & \; \\y & {then} & {\overset{\rightarrow}{v} = \frac{1}{\sqrt{y^{2} + z^{2}}}} \\z & \; & \;\end{matrix}}}\begin{matrix}{- \left( {y^{2} + z^{2}} \right)} \\{xy} \\{xz}\end{matrix}},} & \lbrack 20\rbrack \\{{{{\overset{\rightarrow}{w} = \frac{1}{\sqrt{y^{2} + z^{2}}}}}\begin{matrix}0 \\{- z} \\y\end{matrix}}{and}} & \; \\{P = \begin{bmatrix}\overset{\rightarrow}{u} & \overset{\rightarrow}{v} & \overset{\rightarrow}{w}\end{bmatrix}} & \lbrack 21\rbrack \\{{{In}\mspace{14mu}\lbrack 18\rbrack},} & \; \\{{{{{{{{{M_{1} = {m_{1}{f_{1}(t)}}}}\begin{matrix}\alpha_{1} \\\beta_{1} \\\gamma_{1}\end{matrix}\mspace{31mu} M_{2}} = {m_{2}{f_{2}(t)}}}}\begin{matrix}\alpha_{2} \\\beta_{2} \\\gamma_{2}\end{matrix}\mspace{31mu} M_{1}} = {m_{3}{f_{3}(t)}}}}\begin{matrix}\alpha_{3} \\\beta_{3} \\\gamma_{3}\end{matrix}} & \lbrack 22\rbrack\end{matrix}$are the dipolar moments of the transmitting coils, the amplitude ofwhich change substantially over time according to the functionsf_(j)(t), f₂(t), f₃(t) imposed by the currents circulating in the coils.

m₁ m₂, m₃ are the multiplicative terms of amplitudes of the magneticmoments that depend on the units chosen, the gains of the currentamplifiers E-2, α_(i), β_(i), γ_(i) the direction coefficients (cosines)of the collinear unit vectors of the magnetic moments (axes ofrevolution) of the coils, and f₁(t), f₂(t), f₃(t) represent thevariations of the standardized measurements proportional to the magneticinductions emitted over time by each transmitting coil. The measurementsof emitted inductions are taken by the sensors E-3, secured to thetransmitter E, as shown in FIG. 4, and are proportional to _(L). Theoutput V_(E3) of the sensors E-3 is either digitalized by the CAN blockof the processor for the three axes and digitally incorporated intotherein, or, according to a preferred mode of embodiment of FIG. 4, itis first incorporated by an analog amplifier E-3-2, then digitalized bythe CAN 4-1 of the processor 4 and each of the channels is standardizedby a coefficient determined in the factory in a manner known by theperson skilled in the art, such that the values thus standardizedcorrespond to the physical units and to the nominal values thereof. Thecoefficients α_(i), β_(i), γ_(i) are determined in the factory bycalibration procedures on factory test bench using methods known by theperson skilled in the art.

The functions {right arrow over (X)}_(U)=[X_(U1), X_(U2), X_(U3)]^(t)thus digitalized, proportional to the functions f₁(t), f₂(t), f₃(t) aretherefore the images of the fields emitted by the three coils: byre-writing [18], if {right arrow over (X_(P))} is the vector {rightarrow over (O_(E)O_(C))}B _(C)(t)=[R _(c/e)(t)]^(t) B({right arrow over (X)} _(P))[M ₁ X_(U1)(t)+M ₂ X _(U2)(t)+M ₃ X _(U3)(t)]B({right arrow over (X)} _(P))=[P][H][P] ^(t)  [23]Or again if it is noted A=[R _(c/e)(t)]^(t) B({right arrow over (X)}_(P))  [23-bis]

$\begin{matrix}\left. {{{{{{{{Bc}(t)} = {{{\lbrack A\rbrack \cdot \left\lbrack {{X_{U\; 1}(t)} \cdot m_{1} \cdot} \right.}\begin{matrix}\alpha_{1} \\\beta_{1} \\\gamma_{1}\end{matrix}} + {{X_{U\; 2}(t)} \cdot m_{2} \cdot}}}}\begin{matrix}\alpha_{2} \\\beta_{2} \\\gamma_{2}\end{matrix}} + {{X_{U\; 3}(t)} \cdot m_{3} \cdot}}}\begin{matrix}\alpha_{3} \\\beta_{3} \\\gamma_{3}\end{matrix}} \right\rbrack & \lbrack 24\rbrack \\{{{Bc}(t)} = \begin{bmatrix}{{\left( {{A_{11}\alpha_{1}} + {A_{12}\beta_{1}} + {A_{13}\gamma_{1}}} \right)m_{1}{f_{1}(t)}} + {\left( {{A_{11}\alpha_{2}} + {A_{12}\beta_{2}} + {A_{13}\gamma_{2}}} \right)m_{2}{f_{2}(t)}} + {\left( {{A_{11}\alpha_{3}} + {A_{12}\beta_{3}} + {A_{13}\gamma_{3}}} \right)m_{3}{f_{3}(t)}}} \\{{\left( {{A_{21}\alpha_{1}} + {A_{22}\beta_{1}} + {A_{23}\gamma_{1}}} \right)m_{1}{f_{1}(t)}} + {\left( {{A_{21}\alpha_{2}} + {A_{22}\beta_{2}} + {A_{13}\gamma_{2}}} \right)m_{2}{f_{2}(t)}} + {\left( {{A_{21}\alpha_{3}} + {A_{22}\beta_{3}} + {A_{33}\gamma_{3}}} \right)m_{3}{f_{3}(t)}}} \\{{\left( {{A_{31}\alpha_{1}} + {A_{32}\beta_{1}} + {A_{33}\gamma_{1}}} \right)m_{1}{f_{1}(t)}} + {\left( {{A_{31}\alpha_{2}} + {A_{32}\beta_{2}} + {A_{33}\gamma_{2}}} \right)m_{2}{f_{2}(t)}} + {\left( {{A_{31}\alpha_{3}} + {A_{32}\beta_{3}} + {A_{33}\gamma_{3}}} \right)m_{3}{f_{3}(t)}}}\end{bmatrix}} & \left. 25 \right\rbrack\end{matrix}$

This gives three equations to each three unknowns, i.e., nine terms tobe identified. Measuring the three components of B_(c), when there areno disturbances B_(CU) and B_(RM) of [17], the nine terms of {rightarrow over (X)}_(U)=[X_(U1), X_(U2), X_(U3)]^(t) are identified using aconventional least square method (MSE) or an equivalent recursive method(LMS, RLS).

Therefore, the matrix W is obtained which can be applied in the foil of:

$\begin{matrix}{{W = {{\begin{bmatrix}A_{11} & A_{12} & A_{13} \\A_{21} & A_{22} & A_{23} \\A_{31} & A_{32} & A_{33}\end{bmatrix}\begin{bmatrix}\alpha_{1} & \alpha_{2} & \alpha_{3} \\\beta_{1} & \beta_{2} & \beta_{3} \\\gamma_{1} & \gamma_{2} & \gamma_{3}\end{bmatrix}}\begin{bmatrix}m_{1} & 0 & 0 \\0 & m_{2} & 0 \\0 & 0 & m_{3}\end{bmatrix}}}{{i.e.\mspace{14mu} W} = {\lbrack A\rbrack C_{E}K_{E}}}} & \lbrack 26\rbrack\end{matrix}$

The two matrices, C_(E) and K_(E) (gains and misalignments) relative tothe transmitting block E-1, are identified in the factory, therefore,the matrix A sought is easily obtained.[A]=W[C _(E) K _(E)]⁻¹  [27]

Knowing A, the position {right arrow over (X)}_(P) of the center of thesensor in the transmitter mark and the rotation R_(C/E) (or directioncosines of the axes of the sensor in the transmitter mark) are obtainedaccording to the methods of prior art. Through the identification of thematrix consisting of the coefficients of the functions of {right arrowover (X)}_(CU)=[X_(U1), X_(U2), X_(U3)]^(t), the demultiplexing of thetransmitting channels was thus carried out by identification of a model,and not by temporal demultiplexing (emissions not simultaneous), or byfrequential demultiplexing (U.S. Pat. No. 6,754,609 to Lescourret andU.S. Pat. No. 6,172,499 to Ashe) or any other demultiplexing.

Model {right arrow over (B)}_(CU/E):

As already seen, {right arrow over (B)}_(CU/E) may be considered as theoutput of a linear filter, the input of which are the inductive fieldsemitted by El and the output is the measurement by the sensor C-1. It istherefore still possible to consider that the output at instant t_(k) isa linear combination of the inputs at instants t_(k)−k_(l)·Te. If it isnoted: {right arrow over(X)}_(CU)(t_(k)−k_(l)T_(e))=[X_(U1)(t_(k)−k_(l)T_(e)),X_(U2)(t_(k)−k_(l)T_(e)), X_(U3)(t_(k)−k_(l)T_(e))]^(t), for eachcomponent i_(c) (i_(c)=1 to 3) of the sensor C-1, the following model isformed:

$\begin{matrix}{{B_{{CU}/E}\left( {i_{c},t_{k}} \right)} = {\sum\limits_{j = 1}^{N_{e}}{\sum\limits_{{k{(i_{c})}} = 0}^{N{(i_{c})}}{{A_{cu}\left( {i_{c},j,k_{i_{c}}} \right)}{X_{cu}\left( {j,{t_{k} - {{k\left( i_{c} \right)}{Te}}}} \right)}}}}} & \lbrack 28\rbrack\end{matrix}$

In general, in the environments of cockpits, there are practically noferromagnetic materials, the FMI effects are therefore low in particularfor the high frequencies and in addition vary substantially in1/(D_(P/E) ³D_(C/P) ³) where D_(P/E) is the transmitter-disturberdistance and D_(C/P) the disturber-sensor C-1 distance. When it ispossible to ignore same, the ECI disturbers are the only disturbers ofwhich the model can be written as a function of the shifts of theemitted fields:

$\begin{matrix}{{\overset{\rightarrow}{X_{CU}}\left( {t_{k} - {k_{1}T_{e}}} \right)} = \left\lbrack {{X_{U\; 1}^{\prime}\left( {t_{k} - {k_{1}T_{e}}} \right)},{X_{U\; 2}^{\prime}\left( {t_{k} - {k_{1}T_{e}}} \right)},{X_{U\; 3}^{\prime}\left( {t_{k} - {k_{1}T_{e}}} \right)}} \right\rbrack^{t}} & \lbrack 29\rbrack \\{\mspace{79mu}{With}} & \; \\{\mspace{79mu}{{X_{Uj}^{\prime}\left( t_{k} \right)} \approx \frac{\left( {{X_{Uj}\left( t_{k} \right)} - {X_{Uj}\left( {t_{k} - T_{e}} \right)}} \right)}{Te}}} & \;\end{matrix}$

Model {right arrow over (B)}_(RM/E):

The reference noise extracted from the signals Sb is {right arrow over({circumflex over (B)})}_(RM)={right arrow over (B)}_(C2)−{circumflexover ({circumflex over (B)})}_(CU). If the variable is called X_(BR)(t_(k))={right arrow over ({circumflex over (B)})}_(RM)(t_(k)), and totake into account the transfer functions between sensors, the model ofthe ambient noise for each component i_(c) of the sensor C-1:B_(EM1)(i_(c), t_(k)), may be applied in the form of a function of thevariables X_(BR)(t_(k)−k_(b)T_(e)):

$\begin{matrix}{{{\hat{B}}_{RM}\left( {i_{c},t_{k}} \right)} = {\sum\limits_{k_{b} = 0}^{k_{b} = {N_{kb}{(i_{c})}}}{{C_{b}\left( {k_{b},i_{c}} \right)}{X_{BR}\left( {t_{k} - {k_{b}T_{e}}} \right)}}}} & \lbrack 30\rbrack\end{matrix}$

Complete Model:

The complete model [17] is written for each component of

$\begin{matrix}{{B_{C}\left( {i_{c},t_{k}} \right)} = {{\sum\limits_{j = 1}^{N_{e}}{\sum\limits_{{k{(i_{c})}} = 0}^{N{(i_{c})}}{{A_{CU}\left( {i_{c},j,k_{i_{c}}} \right)}{X_{CU}\left( {j,{t_{k} - {{k\left( i_{c} \right)}{Te}}}} \right)}}}} + {\sum\limits_{k_{b} = 0}^{k_{b} = {N_{kb}{(i_{c})}}}{{C_{b}\left( {k_{b,}i_{c}} \right)}{X_{BR}\left( {t_{k} - {k_{b}T_{e}}} \right)}}}}} & \lbrack 31\rbrack\end{matrix}$

The number of coefficients and the number of variables are in the numberof Ne*Max_(/ic) (N(i_(c))).

The nine terms of A_(cu)(i_(c),j,0) are the terms of the model in freespace, i.e., without disturbers.

Once all of the coefficients are estimated using a conventional leastsquares method (MSE) or an equivalent recursive method (LMS, RLS,Kalman, etc.) at each transmission cycle T_(obs), the termsA_(cu)(i_(c),j,0) relative to the variables X_(Uj)(t_(k)) form a 3×3matrix identical to W of [26] and which are the coefficients of themodel in free space, since same only represent the inductive fields. Asindicated above, the first position and orientation are deducedtherefrom at instants t_(k) from the magnetic detector insensitive todisturbances. The insensitivity to disturbances arises from the factthat the disclosure implements a complete model of useful signals andmeasured and estimated noises, a model for which the coefficients arenot biased due to the completeness of the model.

The P/O_(EM) information according to FIG. 12A of the insensitivemagnetic orientation and position tracker system known as IM tracker,i.e., the position of the center of the sensor X_(C/E)(t_(n)) and therotation R_(C/E)(t_(n)) of the sensor C-1 are known at instantst_(n)=n*T_(obs), n being a positive integer: effectively, theidentification of the coefficients of the equation [31] being carriedout by the computing block 4-4 is performed on N_(obs) points acquiredat instants t_(k) with t_(n)−t_(n−1)=T_(obs). The latency of theinformation provided is of T_(obs)/2.

C. Inertial and Magnetic Hybridization

One of the aims of the disclosure is presented hereafter, which consistsof compensating the latency of a position/orientation tracker system.The example described concerns a magnetic system but would be applied toany system for detecting the orientation of a mobile body.

When the signal-to-noise ratio input from the magnetic detection systemis not sufficient, either that noise exists that is not taken intoaccount by the model or that noise is added on the sensor C-1, onemethod consists of increasing the number of points to further averagethe noise. Therefore, the latency is increased, which is relativelyharmful for the piloting of aircraft. One aspect of the disclosure is toassociate with the magnetic detection an inertial system, the excellentshort-term properties of which are known, i.e., a very short responsetime, but having long-term shifts, in particular due to bias and biasshifts. The magnetic tracker means has an excellent long-term stabilitybut a response time related to the signal-to-noise ratio, which may beinsufficient in some conditions. The principle of the disclosureconsists of associating, also called hybridizing, the magnetic systemand the inertial system, when the platform has an inertial unitproviding the attitude of the platform at any instant within a fixedinertial reference frame. FIG. 12A indicates prior art that consists ofusing the angular velocities measured on the mobile object and also onthe platform in order to be processed in a Kalman filter. FIG. 12Bdescribes the principle of the disclosure that consists of measuring theangular velocities of the mobile object M, and digitally incorporatingsame in a known manner from time t_(i) (initial time) to time t_(f)(final time) to obtain the rotation of the mobile between the twoinstants in the fixed mark. The acquisition of angular velocities iscarried out by the block C-3-1 in FIG. 3A, consisting of a MEMS sensordelivering digitalized angular velocities at a specific speed T_(g)which is a sub-multiple of T_(obs): T_(g)=T_(obs)/k_(g), k_(g) is apositive integer, t_(i) is, for example, the fraction of time thatfollows the instant of arrival of the information from the magnetictracker means t_(n), i.e., t_(n) ⁺·t_(f) is the instant for which theinformation is desired. In the invention, there are two specificinstants t_(f). The first is the instant t, the second is the instantt_(n)+T_(obs). This will be better understood later.

The rotation thus computed from the initial attitude of the gyrometricsensors C-3-1 at time t_(i) is expressed within the fixed inertialreference frame shown by the mark R_(i) in FIG. 2.

The information from the IM tracker means is available at the output of4-4 and constitutes the first orientation known as R_(ot)(t_(n)=n·T_(obs)). The rotation is T_(C/E) ^(EM) (t_(n)), i.e., therotation of the axes of the mark R_(M) connected to the mobile object Maccording to FIG. 2 expressed in the mark of the transmitter. Knowingthe transfer matrix from the transmitter to the platform R_(E/P) by ameasurement during installation of the transmitter in the platform andthe transfer matrix of R_(M) at the mark of the sensor C-1: R_(C1), theperson skilled in the art knows how to compute the rotation of the markR_(M) relative to R_(P), i.e., R_(M/P) ^(EM). To process the magneticand inertial information, it is necessary to express same in the samemark, for example, the mark R_(i). Therefore, R_(M/I) ^(EM)=R_(P/I)R_(M/P) ^(EM) must be computed. For this, it is necessary to knowR_(P/I), which is none other than the direction cosine matrix of theplatform that is provided by the inertial unit C-3-2 of the platform, ingeneral, in the form of three Euler angles, Yaw ψ, Pitch ⊖ and Roll ϕ,from which, R_(P/I) then R_(M/I) ^(EM) are computed.

The direction cosines of the gyrometers are deduced therefrom in theinertial frame at time t_(i)=t_(n) by the formula:R _(g/i) ^(EM)(t _(n))={circumflex over (R)} _(P/i)(t _(n))·R _(M/P)^(EM)(t _(n))·R _(g/m)  [32]where R_(g/m) is the constant matrix defining the direction cosines ofthe gyrometers in the mobile mark M. The quaternion Q(t_(n)) is deducedfrom R_(g/i) ^(EM) (t_(n)).

The quaternion Q(t_(kg)=t_(n)+k_(g)·T_(g)) obtained by digitalincorporation of the equation of the type {dot over (Q)}=F(ω)Q or in theincorporated form thereof:

$\begin{matrix}{{\hat{Q}\left( t_{kg} \right)} = {\int_{t_{n}}^{t_{kg} = {t_{n} + {k_{g} \cdot T_{g}}}}{\frac{{F\left( {\overset{\hat{\rightarrow}}{\omega}(u)} \right)} \cdot {Q(u)}}{2}{of}\mspace{14mu}{the}}}} & \left\lbrack {33\text{-}a} \right\rbrack\end{matrix}$With the initial condition:{circumflex over (Q)}(t _(n))={circumflexover (Q)} _(i)(t _(n))  [33-b]

It will be seen that initial conditions are the value of the statepredicted by the model at t_(n) to which is added a fraction of theerror between estimated measurement and real measurement.

$\begin{matrix}{{F\left( {\overset{\hat{\rightarrow}}{\omega}}_{(u)} \right)} = \begin{pmatrix}0 & {- {{\hat{\omega}}_{x}(u)}} & {- {{\hat{\omega}}_{y}(u)}} & {- {{\hat{\omega}}_{z}(u)}} \\{{\hat{\omega}}_{x}(u)} & 0 & {+ {{\hat{\omega}}_{z}(u)}} & {- {{\hat{\omega}}_{y}(u)}} \\{{\hat{\omega}}_{y}(u)} & {- {{\hat{\omega}}_{z}(u)}} & 0 & {+ {{\hat{\omega}}_{x}(u)}} \\{{\hat{\omega}}_{z}(u)} & {+ {{\hat{\omega}}_{y}(u)}} & {- {{\hat{\omega}}_{x}(u)}} & 0\end{pmatrix}} & \left\lbrack {33\text{-}c} \right\rbrack\end{matrix}$Where {circumflex over ({right arrow over (ω)})}={right arrow over(ω)}_(m)−{right arrow over (δ{circumflex over (ω)})},  [33-d]

calculated from the values provided by the gyrometers and corrected ofthe errors of the gyrometers {right arrow over (δ{circumflex over (ω)})}estimated by an optimal estimator of the Kalman type (extended: EKF or“unscented”: UKF) or sub-optimal (“Recursive least squares” of the typeLMS, RLS, etc.) according to a model of errors of the type:{right arrow over (δ{circumflex over (ω)})}={circumflex over (b)} _(ω)+ΔK·{circumflex over ({right arrow over (ω)})}  [34]

where {right arrow over (ω)}_(b) is a random bias and K is the matrix ofgain, misalignment and coupling errors between channels.

The propagation of gyrometric errors is carried out by a dynamic modelof the terms of {right arrow over (δ{circumflex over (ω)})}, sameincorporated as is known to be carried out with a Kalman filter. Bycalling dQ the error between the value Q_(i) ^(EM) (t_(n)) computed bythe magnetic tracker means at time t_(n) and Q(t_(n)) incorporated fromt to t_(n), the propagation state vector of the errors is for example ofthe type:

$\begin{matrix}{X = {\begin{bmatrix}Q^{t} & {dQ}^{t} & b_{\omega}^{t} & {\Delta\; K^{t}}\end{bmatrix}^{t}:{\overset{.}{Q}\frac{1}{2}{F\left( {\overset{\hat{\rightarrow}}{\omega}}_{(t)} \right)}{Q(t)}}}} & \lbrack 35\rbrack \\{{d\hat{\overset{.}{Q}}} = {{\frac{1}{2}{F\left( \hat{\omega} \right)}d\hat{Q}} + {\frac{1}{2}{C\left( \hat{Q} \right)}\overset{\_}{\delta\omega}}}} & \lbrack 36\rbrack \\{{\overset{.}{\overset{\rightarrow}{b}}}_{\omega} = {{{Vg}\mspace{14mu}{ou}\mspace{14mu}{\overset{.}{\overset{\rightarrow}{b}}}_{\omega}} = {{{- \frac{1}{Tg}}{\overset{\rightarrow}{b}}_{\omega}} + {Vg}}}} & \lbrack 37\rbrack \\{{\Delta\overset{.}{K}} = {{V_{K}\mspace{14mu}{ou}\mspace{14mu}\Delta\overset{.}{K}} = {{{- \frac{1}{T_{k}}}\Delta\; K} + V_{K}}}} & \lbrack 38\rbrack \\{\hat{Y} = {d\hat{Q}}} & \left\lbrack {39\text{-}a} \right\rbrack\end{matrix}$Y=dQ+v measures  [39-b]

With

$\begin{matrix}{{C(Q)} = \begin{bmatrix}{- Q_{1}} & {- Q_{2}} & {- Q_{3}} \\{+ Q_{0}} & {- Q_{1}} & {+ Q_{2}} \\{+ Q_{3}} & {+ Q_{0}} & {- Q_{1}} \\{{- Q_{2}}\;} & {+ Q_{1}} & {+ Q_{0}}\end{bmatrix}} & \lbrack 40\rbrack\end{matrix}$

v, Vg, Vk are superimposed additive Gaussian noises centered accordingto the characteristics of the fluctuations of the terms {right arrowover (b)}_(ω) and K of [38-a and 38-b] and the error provided by themagnetic detection system.

Equations [35] to [38] may be digitally incorporated in various mannersor be applied in the form of recurrent matrix equations. At each instantt_(n), the parameters of {right arrow over (δω)} are reset usingformulas known by the person skilled in the art depending on the filterchosen, for example, the Kalman filter.

In this hypothesis, the resetting formula is of the type:X(t _(n) ⁺)=X(t _(n) ⁻)+K _(n)(Y−Ŷ)  [41]

If the Kalman filter (of the standard or extended (EKF) or unscented(UKF) type is used, K_(n) is obtained using well-known formulas(prediction and resetting of the covariance matrix). If K_(n)=1, theprediction model is not trusted: resetting consists of initializing theincorporation with {circumflex over (Q)}_(i) ^(EM) (t_(n)). If K_(n)=0,the measures are not trusted, which are not taken into account.Adjustment of the gain does not form part of the disclosure, inparticular because it depends a great deal on experimental conditions(noise, quality of the sensors, etc.).

The compensation of the latency is performed in the following manner:After the resetting of the filter according to [41] at the instant t_(n)⁺ the equations [35] to [38] are incorporated over a timet_(kg)−T_(obs)/2 up to t_(kg) (the current time), by using the rawangular velocities stored in memory over the time interval, andcorrected according to [33-d]. The initial value of Q is the value resetat t_(n) ⁺. A new value of {circumflex over (Q)}(t_(kg)) is obtained.Then, from t_(kg) to

${t_{kg} + \frac{T_{obs}}{2}},$at each new acquisition of {right arrow over (ω)}_(m), {circumflex over(Q)}(t_(kg)) is computed according to the same formulas [35] to [38] upto the new resetting value Q(t_(n+1)) date of the arrival of the neworientation of the tracker system (first orientation). Thus, thecompensation has been carried out.

The direction cosine matrix R_(g/i) (t_(kg)) is computed defining theattitude of the gyrometers in the fixed mark and computed from thequaternion {circumflex over (Q)}(t_(kg))=[q₀ q₁ q₂ q₃]^(t) of [33] usingthe following formula:

$\begin{matrix}{R_{g/i} = \begin{bmatrix}{q_{0}^{2} + q_{1}^{2} - q_{3}^{2} - q_{4}^{2}} & {2\left( {{q_{1}^{2}q_{2}^{2}} - {q_{0}^{2}q_{3}^{2}}} \right)} & {2\left( {{q_{1}^{2}q_{3}^{2}} + {q_{0}^{2}q_{2}^{2}}} \right)} \\{2\left( {{q_{1}^{2}q_{2}^{2}} + {q_{0}^{2}q_{3}^{2}}} \right)} & {q_{0}^{2} + q_{2}^{2} - q_{3}^{2} - q_{1}^{2}} & {2\left( {{q_{3}^{2}q_{2}^{2}} + {q_{0}^{2}q_{1}^{2}}} \right)} \\{2\left( {{q_{1}^{2}q_{3}^{2}} - {q_{0}^{2}q_{2}^{2}}} \right)} & {2\left( {{q_{3}^{2}q_{2}^{2}} + {q_{0}^{2}q_{1}^{2}}} \right)} & {q_{0}^{2} + q_{3}^{2} - q_{1}^{2} - q_{2}^{2}}\end{bmatrix}} & \lbrack 42\rbrack\end{matrix}$

The matrix defining the direction cosines of the mark of the mobileobject M relative to the reference mark (mark of the platform R_(P)) isthen computed using the expression:R _(m/p)(t _(kg))=R _(p/i) ^(t)(t _(kg)){circumflex over (R)} _(g/i)(t_(kg))R _(g/m) ^(t)  [43]

The second orientation may be defined by the Euler angles extracted fromthe matrix Rm/p (t_(kg)) using formulas known by the person skilled inthe art.

The method makes it possible, on one hand, to provide at very high speed(in the order of 10 times faster) the estimation of the secondorientation, which minimizes the delay between the provision of theinformation computed and the use thereof by the system that carries outthe acquisition thereof at any periodicity and in a manner notsynchronized with t_(n), and, on the other hand, the compensation of thelatency by the computation of the trajectory of (t_(kg)−T_(obs)/2) att_(kg) thanks to the storing in memory and correction of the gyrometricspeeds of (t_(kg)−T_(obs)/2) at t_(kg).

Applications

Applications of the invention are mainly those for which significantaccuracy is necessary for the position and orientation of a bodyrelative to another body taken for reference in the presence of strongelectromagnetic disturbances. The position and orientation of the helmetof civilian and military aircraft pilots without using magnetic maps isa first application. Numerous applications in surgery, in simulators,capture of movements and video games, etc., are possible.

The invention claimed is:
 1. A system for contactless determination of aposition and orientation of a first mobile object (M) relative to areference mark (R_(P)) carried by a second fixed or mobile object (P),in a disturbed electromagnetic environment, comprising: at least oneelectromagnetic sensor and at least one inertial sensor connected to thefirst mobile object; at least one transmitter comprising at least onetransmitting antenna and at least one inertial unit including inertialsensors, the at least one transmitter connected to the second fixed ormobile object, the at least one transmitting antenna comprisingferromagnetic cores having effective relative magnetic permeabilityhigher than 10, incorporating sensors for measuring a magnetic fieldX_(u) actually emitted by axes of the ferromagnetic cores that providesvariables for measuring an actual field emitted by the at least onetransmitter; at least one reference electromagnetic sensor connected tothe second fixed or mobile object; and a computer for determining anorientation and position of the first mobile object depending on signalsprovided by the sensors and inertial sensors.
 2. The system according toclaim 1, wherein the at least one transmitter is configured fortransmitting magnetic induction(s), the at least one transmittingantenna including Ne transmitting coils having non-parallel axes ofsymmetry, the axes of symmetry forming a reference mark, wherein Ne isgreater than or equal to 2; wherein the at least one electromagneticsensor comprises Nc non-parallel receiving coils, the non-parallelreceiving coils being sensitive to an ambient magnetic field resultingfrom a vector sum of fields emitted by the at least one transmitter anddisturbing magnetic fields generated by electric currents existing inthe disturbed electromagnetic environment and by ferromagneticmagnetizations, the at least one electromagnetic sensor forming ameasurement mark, wherein Nc is greater than or equal to 2, wherein theproduct of Nc and Ne is greater than or equal to 6; wherein the computeris coupled to: a first analog/digital conversion means for carrying outacquisition of analog signals at discrete times t_(k)=k*T_(e) and asecond digital/analog conversion means for generating predeterminedcurrents injected into the at least one transmitter; the transmittingantenna comprising the ferromagnetic cores having effective relativemagnetic permeability higher than 10, incorporating the sensors formeasuring the magnetic field X_(u) actually emitted by the ferromagneticcores that provide variables X_(u)(j, t_(k)−k(i_(c)) T_(e)) for j=1 toNe and i_(c)=1 to Nc; and means for extracting a signal correlated witha surrounding noise X_(BR)(t_(k)−k_(b)T_(e)) from the sensors connectedto the second fixed or mobile object in order to form with the magneticfield X_(u) a complete model of the measured fields making it possibleto extract, without disturbers, while demultiplexing channels emittedsimultaneously, which makes it possible to compute the orientation andposition of the first mobile object; and further comprising means forhybridization comprising: i) the at least one inertial sensor connectedto the first mobile object and forming an inertial sub-assembly for IMUgyrometric measurements; ii) means for acquiring attitude information ofan INS navigation unit connected to the second fixed or mobile object;and iii) a system for detecting magnetic tracker posture connected tothe first mobile object and making it possible to cancel out the latencyof the means for detecting position and for providing orientationinformation by computing the incorporation of a differential systemgoverning the dynamics of the attitude of the object and that of sensorerrors.
 3. The system according to claim 2, wherein currents controlledby the computer are simultaneously emitted on three axes of symmetry ofthe Ne transmitting coils continuously or discontinuously according to acyclical temporal pattern of durationT_(obs)−T_(off)=N_(obs)·T_(e)−T_(off), the computer estimates,continuously and in real time with an output recurrence frequencyF_(out) proportional to $\frac{1}{T_{obs}}$ equal or higher than thefrequencies for refreshing video images, parameters of an analyticalmodel of the vector sum of all of the fields present in the disturbedelectromagnetic environment, the variables of the model being deduced:from measurements taken by a third transmitting sub-assembly of the atleast one transmitter providing the j signals Xu_(j)(t_(k)) proportionalto the emitted inductions, from the computation of variables of the typeX_(u)(j, t_(k)−k(i_(c)) T_(e)) the linear combination of which is themodel of the disturbances correlated with the transmission flux, andfrom the estimation of the signal sum of the disturbances radiated fromthe disturbed electromagnetic environment {circumflex over(B)}_(RM)(t_(k)) not correlated with the fields emitted by the coils ofthe at least one transmitter, and either from the measurements of thereference electromagnetic sensor or extracted from the measurements ofthe signal from the at least one electromagnetic sensor during the timeT_(off) for switching off the transmission.
 4. The system according toclaim 2, wherein the Ne transmitting coils are wound around a cubic orspherical ferromagnetic core comprising cylinders or parallelepipeds, alength-to-diameter or length-to-width ratio of which is higher than 10and the magnetic permeability is higher than 2000, the cylinders orparallelepipeds being interlocked in a substantially identical manneraccording to three directions defined by the axes of symmetry of thecoil windings and in such a way that a barycenter of the ferromagneticcore of each axis is as close as possible to a common center of thethree coils.
 5. The system according to claim 2, wherein a secondorientation is computed in the following manner: at timest_(k)=k·T_(obs), the quaternion Q(t_(k)) defining the attitude of the atleast one inertial sensor in a frame of the reference mark of the atleast one transmitting antenna is computed from the terms of thematrices of direction cosinesR _(g/i) ^(EM)(t _(k))={circumflex over (R)} _(p/i)(t _(k))·R _(m/p)^(EM)(t _(k))·R _(g/m) the quaternion Q(t_(kg)=t_(k)+k_(g)·T_(g))obtained by digital incorporation of the equation Q(t_(kg))=${{Q\left( t_{k} \right)} + {\int_{t_{k}}^{t_{kg} = {t_{k} + {k_{g} \cdot T_{g}}}}{\frac{{A\left( {{\overset{\hat{\rightarrow}}{\omega}}_{m}(u)} \right)} \cdot {Q(u)}}{2}\ d\; u}}},$with Q(t_(k)) being taken from the resetting of the state vector X ofthe type X(t_(n) ⁺)=X(t_(n) ⁻)+K_(n) (Y−Ŷ) during reception of theorientation R_(m/p) ^(EM) (t_(k)) giving the measurement where${A\left( {{\overset{\hat{\rightarrow}}{\omega}}_{m}(u)} \right)} = \begin{pmatrix}0 & {- {{\hat{\omega}}_{mx}(u)}} & {- {{\hat{\omega}}_{my}(u)}} & {- {{\hat{\omega}}_{mz}(u)}} \\{{\hat{\omega}}_{mx}(u)} & 0 & {+ {{\hat{\omega}}_{mz}(u)}} & {- {{\hat{\omega}}_{my}(u)}} \\{{\hat{\omega}}_{my}(u)} & {- {{\hat{\omega}}_{mz}(u)}} & 0 & {{\hat{\omega}}_{mx}(u)} \\{{\hat{\omega}}_{mz}(u)} & {{\hat{\omega}}_{my}(u)} & {- {{\hat{\omega}}_{mx}(u)}} & 0\end{pmatrix}$ with {circumflex over ({right arrow over (ω)})}={rightarrow over (ω)}_(m)−{right arrow over (δ{circumflex over (ω)})},calculated from the values {right arrow over (ω)}_(m) provided by the atleast one inertial sensor and corrected of errors of the at least oneinertial sensor {right arrow over (δ{circumflex over (ω)})} estimated byan optimal estimator of the Kalman or sub-optimal type (“Least recursivesquares” of the type LMS and RLS) according to a model for propagationof errors of the type {right arrow over (δ{circumflex over (ω)})}={rightarrow over (ω)}_(b)+K·{right arrow over (ω)}_(m) where {right arrow over(ω)}_(b) is a random bias and K the matrix of gain, misalignment andcoupling errors between channels; the direction cosine matrixR_(g/i)(t_(kg)) defining the attitude in a fixed mark provided by the atleast one inertial unit is computed from the formula$R_{g/i} = \begin{pmatrix}{q_{0}^{2} + q_{1}^{2} - q_{3}^{2} - q_{4}^{2}} & {2\left( {{q_{1}^{2}q_{2}^{2}} - {q_{0}^{2}q_{3}^{2}}} \right)} & {2\left( {{q_{1}^{2}q_{3}^{2}} + {q_{0}^{2}q_{2}^{2}}} \right)} \\{2\left( {{q_{1}^{2}q_{2}^{2}} + {q_{0}^{2}q_{3}^{2}}} \right)} & {q_{0}^{2} + q_{2}^{2} - q_{3}^{2} - q_{1}^{2}} & {2\left( {{q_{3}^{2}q_{2}^{2}} + {q_{0}^{2}q_{1}^{2}}} \right)} \\{2\left( {{q_{1}^{2}q_{3}^{2}} - {q_{0}^{2}q_{2}^{2}}} \right)} & {2\left( {{q_{3}^{2}q_{2}^{2}} + {q_{0}^{2}q_{1}^{2}}} \right)} & {q_{0}^{2} + q_{3}^{2} - q_{1}^{2} - q_{2}^{2}}\end{pmatrix}$ where Q(t_(kg))=[q₀ q₁ q₂ q₃]^(t); the second orientationprovided at t_(kg) is defined by the direction cosine matrix R_(m/p)(t_(kg)) defining the attitude of the first mobile object relative tothe reference mark is then computed using the expressionR _(m/p)(t _(kg))=R _(p/i) ^(t)(t _(kg)){circumflex over (R)} _(p/i)(t_(kg))R _(g/m) ^(t); and the second orientation being provided by theEuler angles extracted from the matrix R_(m/p) (t_(kg)).
 6. The systemaccording to 2, wherein the first mobile object comprises a helmet. 7.The system according to claim 3, wherein the parameters A(i_(c),j) ofthe analytical model determined relative to the terms X_(U) _(j) (t_(k))and to measurement axis i_(c) of the at least one electromagnetic sensorprovide the terms of the dipolar or multipolar model of the inductivemagnetic fields from the terms of which the computer determines a firstvalue of the position and orientation of the sensor attached to thefirst mobile object on each transmission cycle T_(obs), the orientationdefined by three Euler angles Yaw Y, Pitch P, and Roll R.
 8. The systemaccording to claim 3, wherein the predetermined currents injectedthrough the Ne transmitting coils generate predetermined inductionfluxes F_(j)(t) characteristic of each axis of the coils and cycles ofperiod T_(obs), the value of which is close to periods for refreshingdisplay screens, are such that the induction flux values continuously ordiscontinuously measured by the third transmitting sub-assembly and thendigitized form temporal series that are not linearly dependent so as toform a reversible correlation matrix.
 9. The system according to claim3, wherein currents injected by the at least one transmitter result froma large loop gain control of a direct chain, a setpoint of which is acyclical signal generated digital/analogue conversion means in thecomputer, the cyclical signal being of constant spectral density(Pseudo-Random Binary Sequence) or dependent on the frequency, and areturn signal subtracted from the setpoint being proportional to theinduction from the third transmitting sub-assembly.
 10. The systemaccording to claim 7, wherein variables defining the portion of themodel linearly dependent on Ne fluxes F_(j)(t) measured, j=1 to Ne,emitted by the Ne transmitting coils and received by the axis i_(c) ofthe at least one electromagnetic sensor, comprises a linear combinationof the type:${B_{{CU}/E}\left( {i_{c},t_{k}} \right)}{\sum\limits_{j = 1}^{N_{e}}{\sum\limits_{k_{(i_{c})} = 0}^{N_{(i_{c})}}{{A_{CU}\left( {i_{c},j,k_{i_{c}}} \right)}{X_{CU}\left( {j,{t_{k} - {{k\left( i_{c} \right)}{Te}}}} \right)}}}}$with${\overset{\rightarrow}{X_{CU}}\left( {t_{k} - {k_{1}T_{e}}} \right)} = \left\lbrack {{X_{U\; 1}\left( {t_{k} - {k_{1}T_{e}}} \right)},{X_{U\; 2}\left( {t_{k} - {k_{1}T_{e}}} \right)},{X_{U\; 3}\left( {t_{k} - {k_{1}T_{e}}} \right)}} \right\rbrack^{t}$in which the terms A_(C)(i_(c),j,k_(i)) for which k_(ic)=0 tend towardthe values proportional to the inductive field that would be measured infree space in the absence of any magnetic disturbances, the othercoefficients representing the values proportional to the inductions ofthe disturbing effects linearly dependent on the induction fluxesemitted.
 11. The system according to claim 1, wherein a model ofalternating signals of the environment of each component i_(c) of the atleast one electromagnetic sensor comprises a sum of signals ofsinusoidal type${B_{ESC}\left( {i_{c},t_{k}} \right)} = {{\sum\limits_{k_{sc} = 1}^{N_{sc}}{{\hat{C}}_{SC}^{re}{\left( {i_{c},k_{sc}} \right) \cdot {\cos\left( {\omega_{k_{sc}}{tk}} \right)}}}} + {{{\hat{C}}_{SC}^{im}\left( {i_{c},k_{sc}} \right)} \cdot {\sin\left( {\omega_{k_{sc}}{tk}} \right)}}}$the frequencies ω_(k) _(sc) of which are estimated during the periods ofnon-emission T_(off) from the signals of the at least oneelectromagnetic sensor to form the variables Xsc of a model grouping thesum of the model {circumflex over (B)}_(EC)(i_(c), t_(k)) and of themodel B_(ESC) (i_(c), t_(k)):$B_{E} = {{\sum\limits_{j = 1}^{N_{e}}{\sum\limits_{k_{i_{c}} = 0}^{N_{i_{c}}}{{{\hat{A}}_{C}\left( {i_{c},j,k_{i_{c}}} \right)} \cdot {X_{C}\left( {i_{c},j,k_{i_{c}}} \right)}}}} + {\sum\limits_{k_{sc} = 1}^{N_{sc}}{{{\hat{C}}_{SC}^{re}\left( {i_{c},k_{sc}} \right)} \cdot {\cos\left( {\omega_{k_{sc}}t_{k}} \right)}}} + {{{\hat{C}}_{SC}^{im}\left( {i_{c},k_{sc}} \right)} \cdot {{\sin\left( {\omega_{k_{sc}}t_{k}} \right)}.}}}$12. The system according to claim 1, wherein a signal measured by thereference electromagnetic sensor B_(Rm)(i_(c),t_(k)) is filtered toobtain reference noise signal {circumflex over (B)}_(Ebr) (i_(c), t_(k))by the following operations: B̂_(RM) = B_(C 2) − B̂_(CU)  with${{\hat{B}}_{RU}\left( {i_{c},t_{k}} \right)} = {\sum\limits_{j = 1}^{N_{e}}\;{\sum\limits_{k_{b} = 0}^{N_{b}}{{A_{BRC}\left( {i_{c},j,k_{b}} \right)} \cdot {{X_{C}\left( {i_{c},j,k_{b}} \right)}.}}}}$